G2-cubic contours Original Research Article

Let View the MathML source be the vertex sequence of a convex polygon and through each View the MathML source choose a line such that View the MathML source and View the MathML source lie on one of its sides, and let View the MathML source be the intersection point of line through View the MathML source and View the MathML source. For any choice View the MathML source of an interior point in each triangle View the MathML source we construct G2-cubic algebraic splines which interpolate the vertices View the MathML source and the points View the MathML source. At each View the MathML source the spline is tangent to the prescribed line at this point and it is contained in the union of the triangles View the MathML source. For any j=0,1,…,n we show how the choice of View the MathML source limits the range of variation of the curvatures at the vertices View the MathML source and View the MathML source. We study the conditions for the curvatures at the specific vertices to vary arbitrarily, hence allowing for the construction of G2-interpolating cubic splines which are as flat or as sharp, as desired at these points. A generalization for nonconvex data sequences is given by breaking the polygon into maximal monotonically convex subsequences. The resulting spline has inflections at user controlled points.